SU(3) ⊃ R(3) Wigner coefficients in the 2s-1d shell

Abstract

Explicit algebraic expressions are given for SU(3) ⊃ R(3) Wigner coefficients, which are of particular interest in p-shell and 2s-1d shell-model calculations. An orthogonal basis tied closely to Elliott's basis is chosen according to a systematic recipe. The Wigner coefficients are those involving the Kronecker products ( λ 1 μ 1) × ( λ 2 μ 2) → ( λ 3 μ 3) in the following cases: 1. (i) ( λ 2 μ 2) = (10), (01) and μ 1 ≦ 4 (arbitrary λ i ), i = 1, 3. (For the case μ i = 4, only auxillary coefficients are tabulated whenever the angular momentum multiplicity is 3. From these the final Wigner coefficients can be calculated for any specific case of interest.) 2. (ii) ( λ 2 μ 2) = (20), (02) and μ i ≦ 3 (arbitrary λ i ), or λ i ≦ 3 (arbitrary μ i ) i = 1, 3. 3. (iii) ( λ 2 μ 2 = (11) and μ i ≦ 3 (arbitrary λ i ), or λ i ≦ 3 (arbitrary μ i ) i = 1, 3 except for ( λ3) × (11) → ( λ3) which is not given. A method is also given whereby coefficients with more complicated (λ 2μ 2) can be calculated from coefficients of type (i) by a build-up process. Some symmetry properties are discussed.